Method, medium and apparatus for quantization encoding and de-quantization decoding using trellis

ABSTRACT

Provided are a method and apparatus for quantization encoding and de-quantization decoding using a trellis. Unlike a trellis coded quantization (TCQ) index, by classifying quantization levels to which cosets are allocated and allocating indexes to the quantization levels so that a coset corresponding to a specific branch in a predetermined state in the trellis can be selected with only indexes without encoding or decoding information on paths, quantization encoding and de-quantization decoding are performed by using a new index.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of Korean Patent Application No.10-2007-0138598, filed on Dec. 27, 2007, in the Korean IntellectualProperty Office, the disclosure of which is incorporated herein in itsentirety by reference.

BACKGROUND

1. Field

One or more embodiments of the present invention relates to quantizationencoding and de-quantization decoding, and more particularly, to amethod, medium and apparatus for quantization and de-quantization usinga trellis.

2. Description of the Related Art

Trellis quantization coding is a type of vector quantization methods, inwhich a vector codebook required for encoding is composed of a scalarcodebook corresponding to each element forming a vector, a trellisstructure is represented by using a convolution coder, and a trellispath for optimal encoding is searched for using a Viterbi algorithm. Atrellis quantization coding scheme has much lower complexity thanunstructured vector quantization.

SUMMARY

One or more embodiments of the present invention provide a method andapparatus for quantization encoding and de-quantization decoding usingtrellis.

According to an aspect of the present invention, there is provided aquantization encoding method comprising: detecting indexes correspondingto an input from a trellis coded quantization (TCQ) codebook; andentropy-encoding the detected indexes, wherein indexes are allocated inthe TCQ codebook by classifying quantization levels to which cosets areallocated so that a coset corresponding to a specific branch can beselected in a predetermined state contained in a trellis by using onlyan index when de-quantization is performed.

According to another aspect of the present invention, there is provideda de-quantization decoding method comprising: restoring indexes byperforming entropy-decoding; detecting cosets included in the restoredindexes from a trellis coded quantization (TCQ) codebook; detecting acoset, which corresponds to a branch connecting between a current stateand a subsequent state from among the detected cosets, from a trellis;and detecting a quantization level corresponding to the restored indexesand the detected coset from the TCQ codebook.

According to another aspect of the present invention, there is provideda method of forming a quantizer, the method comprising: setting cosetsthat are to be used in a trellis and a trellis coded quantization (TCQ)codebook; grouping the set cosets with cosets that cannot coexist withcosets allocated to branches connected to predetermined states; andclassifying and indexing quantization levels contained in the TCQcodebook by using the grouped cosets.

According to another aspect of the present invention, there is provideda quantization encoding apparatus comprising: an index detectordetecting indexes corresponding to an input from a trellis codedquantization (TCQ) codebook; and an entropy encoder entropy-encoding thedetected indexes, wherein indexes are allocated in the TCQ codebook byclassifying quantization levels to which cosets are allocated so that acoset corresponding to a specific branch can be selected in apredetermined state contained in a trellis by using only an index whende-quantization is performed.

According to another aspect of the present invention, there is provideda de-quantization decoding apparatus comprising: an entropy decoderrestoring indexes by performing entropy-decoding; a coset detectordetecting cosets included in the restored indexes from a trellis codedquantization (TCQ) codebook; a path detector detecting a coset, whichcorresponds to a branch connecting between a current state and asubsequent state from among the detected cosets, from a trellis; and aquantization level detector detecting a quantization level correspondingto the restored indexes and the detected coset from the TCQ codebook.

According to another aspect of the present invention, there is providedan apparatus for forming a quantizer, the apparatus comprising: a cosetsetting unit setting cosets that are to be used in a trellis and atrellis coded quantization (TCQ) codebook; a coset configuration unitgrouping the set cosets with cosets that cannot coexist with cosetsallocated to branches connected to predetermined states; and an indexingunit classifying and indexing quantization levels contained in the TCQcodebook by using the grouped cosets.

BRIEF DESCRIPTION OF THE DRAWINGS

These and/or other aspects and advantages will become apparent and morereadily appreciated from the following description of the embodiments,taken in conjunction with the accompanying drawings of which:

FIG. 1 illustrates a block diagram of a convolution encodercorresponding to an 8-state trellis using 4 cosets;

FIG. 2 illustrates a conceptual diagram of an 8-state trellis using 4cosets;

FIG. 3 illustrates a conceptual diagram of a 4-coset trellis codedquantization (TCQ) codebook;

FIG. 4 illustrates a flowchart illustrating a method of forming aquantizer using a new indexing method, according to an embodiment of thepresent invention;

FIG. 5 illustrates a conceptual diagram of an 8-coset TCQ codebook;

FIG. 6 illustrates a block diagram of a convolution encodercorresponding to a 16-state trellis using 4 cosets;

FIG. 7 illustrates a conceptual diagram of a 16-state trellis using 8cosets;

FIG. 8 illustrates a block diagram of a convolution encodercorresponding to a 8-state trellis using 8 cosets;

FIG. 9 illustrates a conceptual diagram of an 8-state trellis;

FIG. 10 illustrates a block diagram of a convolution encodercorresponding to a 16-state trellis using 8 cosets;

FIG. 11 illustrates a conceptual diagram of a 16-state trellis using 4cosets;

FIG. 12 illustrates a conceptual diagram of a 4-coset TCQ codebook inwhich a quantization level is not allocated to ‘0’;

FIG. 13 illustrates a conceptual diagram of an 8-coset TCQ codebook inwhich a quantization level is not allocated to ‘0’;

FIG. 14 illustrates a conceptual diagram of a 4-coset TCQ codebook inwhich a quantization level 0 is allocated as a dead zone;

FIG. 15 illustrates a flowchart illustrating a quantization encodingmethod according to an embodiment of the present invention;

FIG. 16 illustrates a flowchart illustrating a de-quantization decodingmethod according to an embodiment of the present invention;

FIG. 17 illustrates a block diagram of an apparatus for forming aquantizer using a new indexing method, according to an embodiment of thepresent invention;

FIG. 18 illustrates a block diagram of a quantization encoding apparatusaccording to an embodiment of the present invention; and

FIG. 19 illustrates a block diagram of a de-quantization decodingapparatus according to an embodiment of the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Reference will now be made in detail to embodiments, examples of whichare illustrated in the accompanying drawings, wherein like referencenumerals refer to the like elements throughout. In this regard,embodiments of the present invention may be embodied in many differentforms and should not be construed as being limited to embodiments setforth herein. Accordingly, embodiments are merely described below, byreferring to the figures, to explain aspects of the present invention.

According to the embodiments of a quantization encoding method andapparatus according to the present invention, quantization encoding canbe implemented by using a convolution encoder, a trellis, and a trelliscoded quantization (TCQ) codebook.

The convolution encoder receives a path and selects a branch from amongbranches connecting between a predetermined state contained in apredetermined stage and states contained in subsequent stages. FIG. 1 isa block diagram of a convolution encoder corresponding to an 8-statetrellis using 4 cosets. Referring to FIG. 1, the convolution encoderreceives ‘0’ or ‘1’, which is a code indicating a path, through an inputterminal x(n), sequentially and temporarily stores codes z0, z1, and z2indicating previous paths in “Ds”, and outputs a code indicating acoset, which is an identifier allocated to each branch, through outputterminals y₁(n) and y₂(n). For example, cosets corresponding to codesoutput through the output terminals y₁(n) and y₂(n) can be illustratedin Table 1.

TABLE 1 y1(n) y2(n) Coset 0 0 D₀ 0 1 D₁ 1 0 D₂ 1 1 D₃

The convolution encoder corresponds to paths of states included in atrellis. The trellis includes a plurality of states, wherein each statecontained in a predetermined stage is connected through branch(es) to atleast one of a plurality of states contained in a subsequent stage, andeach branch can be identified with a pre-set number of cosets.

For example, FIG. 2 is a conceptual diagram of an 8-state trellis using4 cosets, which corresponds to the convolution encoder illustrated inFIG. 1. In FIG. 2, 0 through 7 correspond to 8 states, and D₀, D₁, D₂,and D₃ correspond to 4 cosets are allocated to respective branches. If acoset, i.e., the former of two cosets allocated to each state, isdetected, a path of x(n) of the convolution encoder illustrated in FIG.1 becomes ‘0’, and the upper one of two branches connected to nodes ofeach state is selected as a path, and if a coset, i.e., the latter oftwo cosets allocated to each state, is detected, the path of x(n) of theconvolution encoder illustrated in FIG. 1 becomes ‘1’, and the lower oneof two branches connected to nodes of each state is selected as a path.If a coset D₀ is detected in a state 4, D₀ corresponds to a coset in thelatter, a lower branch is selected, and a code 1 indicating a path isselected.

Referring to FIGS. 1 and 2 and Table 1, when it is assumed that aninitial state is ‘0’, if codes ‘1’, ‘1’, ‘1’, ‘1’, and ‘0’ indicatingpaths are sequentially input to the convolution encoder illustrated inFIG. 1 through the input terminal x(n), codes output from theconvolution encoder illustrated in FIG. 1 through the output terminalsy₁(n) and y₂(n), cosets illustrated in Table 1 corresponding to thecodes, and states determined by the trellis illustrated in FIG. 2according to the paths input through the input terminal x(n) areillustrated in Table 2.

TABLE 2 x (n) z2 z1 z0 State y₁ (n) y₂ (n) Coset 1 0 0 0 0 1 0 D₂ 1 0 01 1 0 0 D₀ 1 0 1 1 3 0 1 D₁ 1 1 1 1 7 1 1 D₃ 0 1 1 1 7 0 1 D₁

When it is assumed that ‘0’ is initially allocated to z0, z1, and z2, if‘1’ is input through x(n) as a code indicating a path, by outputting ‘1’through y₁(n) and ‘0’ through y₂(n) from the convolution encoderillustrated in FIG. 1, D₂ is selected as a coset corresponding to y₁(n)and y₂(n) from Table 1, and a branch corresponding to D₂ in the state 0contained in the trellis illustrated in FIG. 2 is selected, andaccordingly ‘1’ is selected as a subsequent state. Thereafter, if ‘1’ isinput through x(n), ‘1’ that is the previously input x(n) value isshifted to z0, ‘0’ that is the value previously stored in z0 is shiftedto z1, ‘0’ that is the value previously stored in z1 is shifted to z2,and accordingly, by outputting ‘0’ through y₁(n) and ‘0’ through y₂(n)from the convolution encoder illustrated in FIG. 1, D₀ is selected as acoset corresponding to y₁(n) and y₂(n) from Table 1, and a branchcorresponding to D₀ in the state 1 contained in the trellis illustratedin FIG. 2 is selected, and accordingly ‘3’ is selected as a subsequentstate. Likewise, if ‘1’ is input through x(n) again, by outputting ‘0’through y₁(n) and ‘1’ through y₂(n), D₁ is selected as a coset, andaccordingly ‘7’ is selected as a subsequent state. Thereafter, if ‘1’ isinput through x(n), by outputting ‘1’ through y₁(n) and ‘1’ throughy₂(n), D₃ is selected as a coset, and accordingly ‘7’ is selected as asubsequent state. Finally, if ‘0’ is input through x(n), by outputting‘0’ through y₁(n) and ‘1’ through y₂(n), D₁ is selected as a coset.

Cosets contained in the trellis illustrated in FIG. 2 are allocated torespective quantization levels contained in a TCQ codebook. The TCQcodebook can determine a quantization level corresponding to each input.In addition, in the TCQ codebook, quantization levels continuous in apredetermined unit are classified, and respective indexes are allocatedto the classified quantization levels.

For example, FIG. 3 is a conceptual diagram of a 4-coset TCQ codebook.According to a TCQ index illustrated in FIG. 3, a quantization level ‘0’to which the cosets D₀ and D₃ are allocated is classified as a TCQ index‘0’, a quantization level ‘−1.5’ to which the coset D₂ is allocated, aquantization level ‘−2.5’ to which the coset D₁ is allocated, aquantization level ‘−3.5’ to which the coset D₀ is allocated, and aquantization level ‘4.5’ to which the coset D₃ is allocated areclassified as a TCQ index ‘−1’, and a quantization level ‘+1.5’ to whichthe coset D₁ is allocated, a quantization level ‘+2.5’ to which thecoset D₂ is allocated, a quantization level ‘+3.5’ to which the coset D₃is allocated, and a quantization level ‘+4.5’ to which the coset D₀ isallocated are classified as a TCQ index ‘+1’.

The TCQ codebook is pre-set so that different cosets are allocated toquantization levels contained in a single index excluding an index inwhich the quantization level ‘0’ is included. In other words, the TCQcodebook classifies quantization levels by forming a single index withquantization levels corresponding to a total number of cosets. Forexample, if the total number of cosets is 4, the number of quantizationlevels contained in a single index is set to 4, and different cosets areallocated to the quantization levels. As described above, by allocatingdifferent cosets to quantization levels contained in a single index,each quantization level can be identified in a single index. From a TCQcodebook formed in this method, a TCQ index corresponding to an input isdetected, a path corresponding to a quantization level is detected froma trellis and quantized, and entropy encoding of the detected TCQ indexand path is performed.

However, if the entropy encoding of the detected TCQ index and pathobtained in the method described above is performed, since the pathvaries randomly, it is inefficient in terms of entropy encoding. Thus, anew indexing method described below needs to be considered.

FIG. 4 is a flowchart illustrating a method of forming a quantizer usinga new indexing method, according to an embodiment of the presentinvention.

Referring to FIG. 4, in operation 400, a total number of cosets to beused in a trellis and a TCQ codebook is determined and cosetscorresponding to the total number of cosets are set. In operation 400,the total number of cosets can be determined as 2̂n (n is an integergreater than 2). For example, if the total number of cosets isdetermined as 4, 4 cosets corresponding to D₀, D₁, D₂, and D₃ asillustrated in FIGS. 2 and 3 are set in the trellis and the TCQcodebook, and if if the total number of cosets is determined as 8, 8cosets corresponding to D₀, D₁, D₂, D₃, D₄, D₅, D₆ , and D₇ are set inthe trellis and the TCQ codebook.

In operation 410, union cosets are formed by using the cosets set inoperation 400. The union cosets are formed with cosets that cannotcoexist with cosets that are allocated to branches connected to nodes ofpredetermined states. In other words, cosets allocated to branchesconnected to a node of a predetermined state are not contained in thesame union coset. Table 3 illustrates union cosets formed in a unit of 2cosets.

TABLE 3 First coset Second coset First union coset D₀ D_(K/2) Secondunion coset D_(K/2) D_((K/2)+1) . . . . . . . . . N^(th) union cosetD_((K/2)−1) D_(K−1)

In Table 3, N is an integer greater than 2, and K is a total number ofcosets. For example, the union cosets can be formed with {D₀-D₂, D₁-D₃}in a 4-coset TCQ codebook and formed with {D₀-D₄, D₁-D₅} and {D₂-D₆,D₃-D₇} in an 8-coset TCQ codebook.

In operation 420, quantization levels contained in the TCQ codebook areclassified in a predetermined unit and indexed by using the union cosetsformed in operation 410. When the indexing is performed in operation420, quantization levels contained in a single index are indexed so thatonly cosets contained in another union coset are allocated to eachquantization level. For example, in a 4-coset TCQ codebook in whichunion cosets are formed with {D₀-D₂, D₁-D₃}, quantization levelscorresponding to D₀ and D₂ contained in the same union coset must not becontained together in any index, and D₁ and D₃ as well.

The indexing method used in operation 420 includes a first indexingmethod and a second indexing method described below.

According to the first indexing method, in a first index, indexescorresponding to positive integers are allocated to quantization levelsgreater than ‘0’, indexes corresponding to negative integers areallocated to quantization levels less than ‘0’, and the indexes areallocated symmetrically on ‘0’ so that absolute values of the indexesallocated to the quantization levels greater than ‘0’ and thequantization levels less than ‘0’ are the same with different signs.

For example, a first index is illustrated in the lower side of the4-coset TCQ codebook illustrated in FIG. 3. In the first index,quantization levels greater than ‘0’ are indexed as +1, +2, . . . , +8,quantization levels less than ‘0’ are indexed as −1, −2, . . . , −8, andthe indexes having the same absolute values with different signs areallocated symmetrically on ‘0’. In addition, quantization levelscorresponding to D₀ and D₂ contained in the same union coset are notcontained together in any index, and D₁ and D₃ as well. Thus, in thefirst index, a single index contains the number of quantization levels,which corresponds to a half as compared to the TCQ index as illustratedin FIG. 3.

By using the TCQ indexing method described above, the 4-coset TCQcodebook can be indexed in the first indexing method as represented byusing Equation 1.

$\begin{matrix}{n_{D_{0}} = {n_{D_{3}} = \left\{ {{\begin{matrix}0 & {{{{if}\mspace{14mu} t} = 0};} \\{2t} & {{{{if}\mspace{14mu} t} \neq 0};}\end{matrix}n_{D_{1}}} = {n_{D_{2}} = \left\{ \begin{matrix}{{2t} - 1} & {{{{if}\mspace{14mu} t} > 0};} \\{{2t} + 1} & {{{{if}\mspace{14mu} t} < 0};}\end{matrix} \right.}} \right.}} & \left( {{Equation}\mspace{20mu} 1} \right)\end{matrix}$

Here, n denotes the first index, and t denotes the TCQ index.

According to the second indexing method, in a second index, ‘0’ isallocated to an index containing a smallest number of quantizationlevels by allocating only ‘0’ and positive integers as indexes withoutallocating negative integers as indexes, and according to a sequentialincrease of quantization levels, by allocating indexes corresponding toa sequentially greater positive integer to the quantization levels, theindexes are allocated so that the biggest index is contained in an indexcontaining the biggest quantization levels. Comparing the secondindexing method to the first indexing method, the second indexing methodhas the same method of classifying quantization levels and the samesequence of sequentially indexing from the smallest quantization levelto the biggest quantization level as the first indexing method. However,when indexes are allocated, in the first index, negative integers areallocated to indexes less than ‘0’ and positive integers are allocatedto indexes greater than ‘0’ based on an index containing ‘0’, and in thesecond index, ‘0’ is allocated to an index containing the smallestquantization levels and positive integers are sequentially allocated toindexes till an index containing the biggest quantization levels.

For example, by using the TCQ indexing method described above, the4-coset TCQ codebook can be indexed in the second indexing method asrepresented by using Equation 2.

$\begin{matrix}{n_{D_{0}} = \left\{ {{\begin{matrix}{0,} & {{{{if}\mspace{14mu} t} = 0};} \\{{4t},} & {{{{if}\mspace{14mu} t} > 0};} \\{{{- 4}t} - 1} & {{{{if}\mspace{14mu} t} < 0};}\end{matrix}n_{D_{1}}} = \left\{ {{\begin{matrix}{{4t} - 3} & {{{{if}\mspace{14mu} t} > 0};} \\{{{- 4}t} - 2} & {{{{if}\mspace{14mu} t} < 0};}\end{matrix}n_{D_{2}}} = \left\{ {{\begin{matrix}{{4t} - 2} & {{{{if}\mspace{14mu} t} > 0};} \\{{{- 4}t} - 3} & {{{{if}\mspace{14mu} t} < 0};}\end{matrix}n_{D_{3}}} = \left\{ \begin{matrix}0 & {{{{if}\mspace{14mu} t} = 0};} \\{{{4t} - 1},} & {{{{if}\mspace{14mu} t} > 0};} \\{{- 4}t} & {{{{if}\mspace{14mu} t} < 0};}\end{matrix} \right.} \right.} \right.} \right.} & \left( {{Equation}\mspace{20mu} 2} \right)\end{matrix}$

Here, n denotes the second index, and t denotes the TCQ index.

When the TCQ index, the first index, and the second index describedabove are applied to the 8-state trellis illustrated in FIG. 2 and the4-coset TCQ codebook containing two zero levels, which is illustrated inFIG. 3, Tables 4 and 5 can be obtained. Table 4 illustrates indexes of aunion coset C₀ formed with cosets D₀ and D₂, and Table 5 illustratesindexes of a union coset C₁ formed with cosets D₁ and D₃.

TABLE 4 Coset D₀ D₂ D₂ D₀ D₀ D₂ D₂ D₀ D₀ C₀ = D₀ ∪ D₂ quantization 0.5−1.5 2.5 −3.5 4.5 −5.5 6.5 −7.5 8.5 level TCQ index 0 −1 +1 −1 +1 −2 +2−2 +2 First index 0 −1 +1 −2 +2 −3 +3 −4 +4 Second index 0 1 2 3 4 5 6 78 Path 0 1 1 0 0 1 1 0 0

TABLE 5 Coset D₃ D₁ D₁ D₃ D₃ D₁ D₁ D₃ D₃ C₁ = D₁ ∪ D₃ quantization −0.51.5 −2.5 3.5 −4.5 5.5 −6.5 7.5 −8.5 level TCQ index 0 +1 −1 +1 −1 +2 −2+2 −2 First index 0 +1 −1 +2 −2 +3 −3 +4 −4 Second index 0 1 2 3 4 5 6 78 Path 0 1 1 0 0 1 1 0 0

In addition, when the TCQ index, the first index, and the second indexare applied to an 8-coset TCQ codebook in which no zero level exists,Tables 6 through 9 can be obtained. Table 6 illustrates indexes of aunion coset A₀ formed with cosets D₀ and D₄, Table 7 illustrates indexesof a union coset A₁ formed with cosets D₁ and D₅, Table 8 illustratesindexes of a union coset A₂ formed with cosets D₂ and D₆, and Table 9illustrates indexes of a union coset A₃ formed with cosets D₃ and D₇.

TABLE 6 Coset D₀ D₄ D₄ D₀ D₀ D₄ D₄ D₀ D₀ A₀ = D₀ ∪ D₄ quantization 0.25−1.75 2.25 −3.75 4.25 −5.75 6.25 −7.75 8.25 level TCQ index 0 −1 +1 −1+1 −2 +2 −2 +2 First index 0 −1 +1 −2 +2 −3 +3 −4 +4 Second index 0 1 23 4 5 6 7 8 Path 0 1 1 0 0 1 1 0 0

TABLE 7 Coset D₁ D₅ D₅ D₁ D₁ D₅ D₅ D₁ D₁ A₁ = D₁ ∪ D₅ quantization 0.75−1.25 2.75 −3.25 4.75 −5.25 6.75 −7.25 8.75 level TCQ index 0 −1 +1 −1+1 −2 +2 −2 +2 First index 0 −1 +1 −2 +2 −3 +3 −4 +4 Second index 0 1 23 4 5 6 7 8 Path 0 1 1 0 0 1 1 0 0

TABLE 8 Coset D₆ D₂ D₂ D₆ D₆ D₂ D₂ D₆ D₆ A₂ = D₂ ∪ D₆ quantization −0.751.25 −2.75 3.25 −4.75 5.25 −6.75 7.25 −8.75 level TCQ index 0 +1 −1 +1−1 +2 −2 +2 −2 First index 0 +1 −1 +2 −2 +3 −3 +4 −4 Second index 0 1 23 4 5 6 7 8 Path 0 1 1 0 0 1 1 0 0

TABLE 9 Coset D₇ D₃ D₃ D₇ D₇ D₃ D₃ D₇ D₇ A₃ = D₃ ∪ D₇ quantization −0.251.75 −2.25 3.75 −4.25 5.75 −6.25 7.75 −8.25 level TCQ index 0 +1 −1 +1−1 +2 −2 +2 −2 First index 0 +1 −1 +2 −2 +3 −3 +4 −4 Second index 0 1 23 4 5 6 7 8 Path 0 1 1 0 0 1 1 0 0

Finally, when the TCQ index, the first index, and the second index areapplied to an 8-coset TCQ codebook in which two zero levels exist,Tables 10 through 13 can be obtained. Table 10 illustrates indexes of aunion coset A₀ formed with cosets D₀ and D₄, Table 11 illustratesindexes of a union coset A₁ formed with cosets D₁ and D₅, Table 12illustrates indexes of a union coset A₂ formed with cosets D₂ and D₆,and Table 13 illustrates indexes of a union coset A₃ formed with cosetsD₃ and D₇.

TABLE 10 Coset D₀ D₄ D₄ D₀ D₀ D₄ D₄ D₀ D₀ A₀ = D₀ ∪ D₄ 0 −1.5 2 −3.5 4−5.5 6 −7.5 8 quantization level TCQ index 0 −1 +1 −1 +1 −2 +2 −2 +2First index 0 −1 +1 −2 +2 −3 +3 −4 +4 Second index 0 1 2 3 4 5 6 7 8Path 0 1 1 0 0 1 1 0 0

TABLE 11 Coset D₁ D₅ D₅ D₁ D₁ D₅ D₅ D₁ D₁ A₁ = D₁ ∪ D₅ 0.5 −1 2.5 −3 4.5−5 6.5 −7.5 8.5 quantization level TCQ index 0 −1 +1 −1 +1 −2 +2 −2 +2First index 0 −1 +1 −2 +2 −3 +3 −4 +4 Second index 0 1 2 3 4 5 6 7 8Coset Flag 0 1 1 0 0 1 1 0 0

TABLE 12 Coset D₆ D₂ D₂ D₆ D₆ D₂ D₂ D₆ D₆ A₂ = D₂ ∪ D₆ −0.5 1 −2.5 3−4.5 5 −6.5 7 −8.5 quantization level TCQ index 0 +1 −1 +1 −1 +2 −2 +2−2 First index 0 +1 −1 +2 −2 +3 −3 +4 −4 Second index 0 1 2 3 4 5 6 7 8Path 0 1 1 0 0 1 1 0 0

TABLE 13 Coset D₇ D₃ D₃ D₇ D₇ D₃ D₃ D₇ D₇ A₃ = D₃ ∪ D₇ 0 1.5 −2 3.5 −45.5 −6 7.5 −8 quantization level TCQ index 0 +1 −1 +1 −1 +2 −2 +2 −2First index 0 +1 −1 +2 −2 +3 −3 +4 −4 Second index 0 1 2 3 4 5 6 7 8Path 0 1 1 0 0 1 1 0 0

As described above, when the indexing is performed in the first indexingmethod and the second indexing method, an index containing thequantization level ‘0’ is differently indexed from indexes containingquantization levels excluding ‘0’. The index containing the quantizationlevel ‘0’ can be classified into “two zero level” in which two cosetsare allocated to the quantization level ‘0’, “no zero level” in which nocoset is allocated to the quantization level ‘0’, and “dead-zone” inwhich the quantization level ‘0’ is defined as a dead-zone.

First, as embodiments of a TCQ codebook in which two cosets areallocated to the quantization level ‘0’, the 4-coset TCQ codebook isillustrated in FIG. 3, and the 8-coset TCQ codebook is illustrated inFIG. 5. The 4-coset TCQ codebook illustrated in FIG. 3 can beimplemented by using the convolution encoder of an 8-state trellis codeusing 4 cosets, which is illustrated in FIG. 1, and the 8-state trellisillustrated in FIG. 2, or a convolution encoder of a 16-state trelliscode using 4 cosets, which is illustrated in FIG. 6, and a 16-statetrellis illustrated in FIG. 7. The 8-coset TCQ codebook illustrated inFIG. 5 can be implemented by using a convolution encoder of an 8-statetrellis code using 8 cosets, which is illustrated in FIG. 8, and an8-state trellis illustrated in FIG. 9, or a convolution encoder of a16-state trellis code using 8 cosets, which is illustrated in FIG. 10,and a 16-state trellis illustrated in FIG. 11.

Second, as embodiments of a TCQ codebook in which no coset is allocatedto the quantization level ‘0’, a 4-coset TCQ codebook is illustrated inFIG. 12, and an 8-coset TCQ codebook is illustrated in FIG. 13. The4-coset TCQ codebook illustrated in FIG. 12 can be implemented by usingthe convolution encoder of an 8-state trellis code using 4 cosets, whichis illustrated in FIG. 1, and the 8-state trellis illustrated in FIG. 2,or a convolution encoder of a 16-state trellis code using 4 cosets,which is illustrated in FIG. 6, and a 16-state trellis illustrated inFIG. 7. The 8-coset TCQ codebook illustrated in FIG. 13 can beimplemented by using a convolution encoder of an 8-state trellis codeusing 8 cosets, which is illustrated in FIG. 8, and an 8-state trellisillustrated in FIG. 9, or a convolution encoder of a 16-state trelliscode using 8 cosets, which is illustrated in FIG. 10, and a 16-statetrellis illustrated in FIG. 11.

Third, as embodiments of a TCQ codebook in which the quantization level‘0’ is defined as a dead-zone, a 4-coset TCQ codebook is illustrated inFIG. 14. The 4-coset TCQ codebook illustrated in FIG. 14 can beimplemented by using the convolution encoder of an 8-state trellis codeusing 4 cosets, which is illustrated in FIG. 1, and the 8-state trellisillustrated in FIG. 2, or a convolution encoder of a 16-state trelliscode using 4 cosets, which is illustrated in FIG. 6, and a 16-statetrellis illustrated in FIG. 7.

FIG. 15 is a flowchart illustrating a quantization encoding methodaccording to an embodiment of the present invention.

Referring to FIG. 15, in operation 1500, quantization levels of inputvalues are detected from a TCQ codebook. For example, it is assumed thatquantization is performed by means of the first index by using theconvolution encoder illustrated in FIG. 1, the trellis illustrated inFIG. 2, and the TCQ codebook illustrated in FIG. 12, in operation 1500,when (0.6, −5.1, 0.1, 1.3, −0.9, 5.8, 7.1, −1.1) are input, quantizationlevels (0.5, −5.5, 0.5, 1.5, −0.5, 5.5, 7.5, −1.5) corresponding to therespective input values are detected from the TCQ codebook illustratedin FIG. 12.

In operation 1510, indexes containing the quantization levels detectedin operation 1500 are detected from the TCQ codebook. The indexesdetected in operation 1510 correspond to the first index or the secondindex described above. In more detail, in operation 1510, the firstindex (0, −3, 0, +1, 0, +3, +4, +4, −1) containing the quantizationlevels (0.5, −5.5, 0.5, 1.5, −0.5, 5.5, 7.5, −1.5) detected in operation1500 are detected from the TCQ codebook illustrated in FIG. 12. Whenthis result is represented with bit-plane, Table 14 can be obtained.

TABLE 14 First index 0 −3 0 +1 0 +3 +4 −1 b_(S) 0 1 0 0 0 0 0 1 b₂ 0 0 00 0 0 1 0 b₁ 0 1 0 0 0 1 0 0 b₀ 0 1 0 1 0 1 0 1

In operation 1520, entropy encoding of the indexes detected in operation1510 are performed. Unlike that the TCQ index and information indicatinga path are entropy-encoded together when the TCQ index isentropy-encoded, in operation 1520, only the first index or the secondindex is entropy-encoded without entropy encoding the informationindicating a path.

FIG. 16 is a flowchart illustrating a de-quantization decoding methodaccording to an embodiment of the present invention.

Referring to FIG. 16, in operation 1600, indexes are restored bydemultiplexing a bitstream received from an encoder and entropy-decodingthe demultiplexed bitstream. The indexes restored in operation 1600correspond to the first index or the second index.

In operation 1610, cosets contained in the indexes restored in operation1600 are detected from the TCQ codebook.

In operation 1620, a coset, which matches a coset allocated to a branchconnecting a current state and a subsequent state, is detected fromamong the cosets detected in operation 1610. A branch corresponding tothe coset detected in operation 1620 is determined as a path, and a nodeconnected to the branch becomes the subsequent state. Unlike the TCQindex, even if the information on the path is not input from the encoderin operation 1620, the path can be determined from the trellis becausethe first index or the second index is allocated by setting union cosetsso that a specific branch can be selected in a predetermined state whenquantization levels are indexed in the first index or the second index.In other words, in the first index or the second index, since the unioncosets are formed with cosets that cannot coexist with cosets allocatedto branches connected to a node of a predetermined state and the cosetsallocated to branches connected to a node of a predetermined state arenot contained in the same union coset, a decoder can detect the pathwithout receiving the information on the path.

In operation 1630, de-quantization is performed by detecting aquantization level corresponding to the coset detected in operation 1620from among the quantization levels contained in the indexes restored inoperation 1610.

The flowchart of FIG. 16 will now be described in more detail withconcrete examples. It is assumed that the quantization decoding isperformed by using the convolution encoder corresponding to an 8-statetrellis using 4 cosets, which is illustrated in FIG. 1, the 8-statetrellis illustrated in FIG. 2, and the 4-coset TCQ codebook and thefirst index illustrated in FIG. 12. In addition, it is assumed that aninitial state is set to ‘0’ in the 8-state trellis illustrated in FIG. 2and the indexes restored in operation 1600 are (0, −3, 0, +1).

First, for an index ‘0’ of the first index, in operation 1610, thecosets D₀ and D₃ contained in the index ‘0’ of the first index aredetected from the 4-coset TCQ codebook illustrated in FIG. 12, and inoperation 1620, the coset D₀, which is a coset matching the cosets D₀and D₂ corresponding to the branches that can be selected in the initialstate ‘0’ of the 8-state trellis illustrated in FIG. 2, is selected fromamong the cosets D₀ and D₃ detected in operation 1610, and in operation1630, de-quantization is performed by detecting a quantization level‘0.5’ corresponding to the coset D₀ contained in the index ‘0’ of thefirst index. In addition, since the coset D₀ has been selected inoperation 1620 from among the cosets D₀ and D₂ connected to the initialstate ‘0’, a branch corresponding to the coset D₀ in the state ‘0’ isthe upper branch, and therefore, a subsequent state becomes ‘0’.

Second, for an index ‘−3’ of the first index, in operation 1610, thecosets D₁ and D₂ contained in the index ‘−3’ of the first index aredetected from the 4-coset TCQ codebook illustrated in FIG. 12, and inoperation 1620, the coset D₂, which is a coset matching the cosets D₀and D₂ corresponding to the branches that can be selected in the state‘0’ of the 8-state trellis illustrated in FIG. 2, is selected from amongthe cosets D₁ and D₂ detected in operation 1610, and in operation 1630,de-quantization is performed by detecting a quantization level ‘−5.5’corresponding to the coset D₂ contained in the index ‘−3’ of the firstindex. In addition, since the coset D₂ has been selected in operation1620 from among the cosets D₀ and D₂ connected to the state ‘0’, abranch corresponding to the coset D₂ in the state ‘0’ is the lowerbranch, and therefore, a subsequent state becomes ‘1’.

Third, for an index ‘0’ of the first index, in operation 1610, thecosets D₀ and D₃ contained in the index ‘0’ of the first index aredetected from the 4-coset TCQ codebook illustrated in FIG. 12, and inoperation 1620, the coset D₀, which is a coset matching the cosets D₂and D₀ corresponding to the branches that can be selected in the state‘1’ of the 8-state trellis illustrated in FIG. 2, is selected from amongthe cosets D₀ and D₃ detected in operation 1610, and in operation 1630,de-quantization is performed by detecting a quantization level ‘0.5’corresponding to the coset D₀ contained in the index ‘0’ of the firstindex. In addition, since the coset D₀ has been selected in operation1620 from among the cosets D₂ and D₀ connected to the state ‘1’, abranch corresponding to the coset D₀ in the state ‘1’ is the lowerbranch, and therefore, a subsequent state becomes ‘3’.

Fourth, for an index ‘+1’ of the first index, in operation 1610, thecosets D₁ and D₂ contained in the index ‘−3’ of the first index aredetected from the 4-coset TCQ codebook illustrated in FIG. 12, and inoperation 1620, the coset D₁, which is a coset matching the cosets D₃and D₁ corresponding to the branches that can be selected in the state‘3’ of the 8-state trellis illustrated in FIG. 2, is selected from amongthe cosets D₁ and D₂ detected in operation 1610, and in operation 1630,de-quantization is performed by detecting a quantization level ‘1.5’corresponding to the coset D₁ contained in the index ‘+1’ of the firstindex. In addition, since the coset D₁ has been selected in operation1620 from among the cosets D₃ and D₁ connected to the state ‘3’, abranch corresponding to the coset D₁ in the state ‘3’ is the lowerbranch, and therefore, a subsequent state becomes ‘7’.

FIG. 17 is a block diagram of an apparatus for forming a quantizer usinga new indexing method, according to an embodiment of the presentinvention. Referring to FIG. 17, the apparatus according to the currentembodiment includes a coset number determiner 1700, a union coset former1710, and an indexing unit 1720.

The coset number determiner 1700 determines a total number of cosets tobe used in a trellis and a TCQ codebook and sets cosets according to thedetermined number. The coset number determiner 1700 can determine thetotal number of cosets as 2̂n (n is an integer greater than 2). Forexample, if the total number of cosets is determined as 4, 4 cosetscorresponding to D₀, D₁, D₂, and D₃ as illustrated in FIGS. 2 and 3 areset in the trellis and the TCQ codebook, and if the total number ofcosets is determined as 8, 8 cosets corresponding to D₀, D₁, D₂, D₃, D₄,D₅, D₆, and D₇ are set in the trellis and the TCQ codebook.

The union coset former 1710 forms union cosets by using the cosets setby the coset number determiner 1700. The union cosets are formed withcosets that cannot coexist with cosets that are allocated to branchesconnected to nodes of predetermined states. In other words, cosetsallocated to branches connected to a node of a predetermined state arenot contained in the same union coset. Table 15 illustrates union cosetsformed in a unit of 2 cosets.

TABLE 15 First coset Second coset First union coset D₀ D_(K/2) Secondunion coset D_(K/2) D_((K/2)+1) . . . . . . . . . N^(th) union cosetD_((K/2)−1) D_(K−1)

In Table 3, N is an integer greater than 2, and K is a total number ofcosets. For example, the union cosets can be formed with {D₀-D₂, D₁-D₃}in a 4-coset TCQ codebook and formed with {D₀-D₄, D₁-D₅} and {D₂-D₆,D₃-D₇} in an 8-coset TCQ codebook.

The indexing unit 1720 performs indexing by classifying quantizationlevels contained in the TCQ codebook in a predetermined unit by usingthe union cosets formed by the union coset former 1710. When theindexing is performed by the indexing unit 1720, quantization levelscontained in a single index are indexed so that only cosets contained inanother union coset are allocated to each quantization level. Forexample, in a 4-coset TCQ codebook in which union cosets are formed with{D₀-D₂, D₁-D₃}, quantization levels corresponding to D₀ and D₂ containedin the same union coset must not be contained together in any index, andD₁ and D₃ as well.

The indexing method used by the indexing unit 1720 includes a firstindexing method and a second indexing method described below.

According to the first indexing method, in a first index, indexescorresponding to positive integers are allocated to quantization levelsgreater than ‘0’, indexes corresponding to negative integers areallocated to quantization levels less than ‘0’, and the indexes areallocated symmetrically on ‘0’ so that absolute values of the indexesallocated to the quantization levels greater than ‘0’ and thequantization levels less than ‘0’ are the same with different signs.

For example, the first index is illustrated in the lower side of the4-coset TCQ codebook illustrated in FIG. 3. In the first index,quantization levels greater than ‘0’ are indexed as +1, +2, . . . , +8,quantization levels less than ‘0’ are indexed as −1, −2, . . . , −8, andthe indexes having the same absolute values with different signs areallocated symmetrically on ‘0’. In addition, quantization levelscorresponding to D₀ and D₂ contained in the same union coset are notcontained together in any index, and D₁ and D₃ as well. Thus, in thefirst index, a single index contains the number of quantization levels,which corresponds to a half as compared to the TCQ index as illustratedin FIG. 3.

By using the TCQ indexing method described above, the 4-coset TCQcodebook can be indexed in the first indexing method as represented byusing Equation 3.

$\begin{matrix}{n_{D_{0}} = {n_{D_{3}} = \left\{ {{\begin{matrix}0 & {{{{if}\mspace{14mu} t} = 0};} \\{2t} & {{{{if}\mspace{14mu} t} \neq 0};}\end{matrix}n_{D_{1}}} = {n_{D_{2}} = \left\{ \begin{matrix}{{2t} - 1} & {{{{if}\mspace{14mu} t} > 0};} \\{{2t} + 1} & {{{{if}\mspace{14mu} t} < 0};}\end{matrix} \right.}} \right.}} & \left( {{Equation}\mspace{20mu} 3} \right)\end{matrix}$

Here, n denotes the first index, and t denotes the TCQ index.

According to the second indexing method, in a second index, ‘0’ isallocated to an index containing a smallest number of quantizationlevels by allocating only ‘0’ and positive integers as indexes withoutallocating negative integers as indexes, and according to a sequentialincrease of quantization levels, by allocating indexes corresponding toa sequentially greater positive integer to the quantization levels, theindexes are allocated so that the biggest index is contained in an indexcontaining the biggest quantization levels. Comparing the secondindexing method to the first indexing method, the second indexing methodhas the same method of classifying quantization levels and the samesequence of sequentially indexing from the smallest quantization levelto the biggest quantization level as the first indexing method. However,when indexes are allocated, in the first index, negative integers areallocated to indexes less than ‘0’ and positive integers are allocatedto indexes greater than ‘0’ based on an index containing ‘0’, and in thesecond index, ‘0’ is allocated to an index containing the smallestquantization levels and positive integers are sequentially allocated toindexes till an index containing the biggest quantization levels.

For example, by using the TCQ indexing method described above, the4-coset TCQ codebook can be indexed in the second indexing method asrepresented by using Equation 4.

$\begin{matrix}{n_{D_{0}} = \left\{ {{\begin{matrix}{0,} & {{{{if}\mspace{14mu} t} = 0};} \\{{4t},} & {{{{if}\mspace{14mu} t} > 0};} \\{{{- 4}t} - 1} & {{{{if}\mspace{14mu} t} < 0};}\end{matrix}n_{D_{1}}} = \left\{ {{\begin{matrix}{{4t} - 3} & {{{{if}\mspace{14mu} t} > 0};} \\{{{- 4}t} - 2} & {{{{if}\mspace{14mu} t} < 0};}\end{matrix}n_{D_{2}}} = \left\{ {{\begin{matrix}{{4t} - 2} & {{{{if}\mspace{14mu} t} > 0};} \\{{{- 4}t} - 3} & {{{{if}\mspace{14mu} t} < 0};}\end{matrix}n_{D_{3}}} = \left\{ \begin{matrix}0 & {{{{if}\mspace{14mu} t} = 0};} \\{{{4t} - 1},} & {{{{if}\mspace{14mu} t} > 0};} \\{{- 4}t} & {{{{if}\mspace{14mu} t} < 0};}\end{matrix} \right.} \right.} \right.} \right.} & \left( {{Equation}\mspace{20mu} 4} \right)\end{matrix}$

Here, n denotes the second index, and t denotes the TCQ index.

When the TCQ index, the first index, and the second index describedabove are applied to the 8-state trellis illustrated in FIG. 2 and the4-coset TCQ codebook containing two zero levels, which is illustrated inFIG. 3, Tables 16 and 17 can be obtained. Table 16 illustrates indexesof a union coset C₀ formed with cosets D₀ and D₂, and Table 17illustrates indexes of a union coset C₁ formed with cosets D₁ and D₃.

TABLE 16 Coset D₀ D₂ D₂ D₀ D₀ D₂ D₂ D₀ D₀ C₀ = D₀ ∪ D₂ quantization 0.5−1.5 2.5 −3.5 4.5 −5.5 6.5 −7.5 8.5 level TCQ index 0 −1 +1 −1 +1 −2 +2−2 +2 First index 0 −1 +1 −2 +2 −3 +3 −4 +4 Second index 0 1 2 3 4 5 6 78 Path 0 1 1 0 0 1 1 0 0

TABLE 17 Coset D₃ D₁ D₁ D₃ D₃ D₁ D₁ D₃ D₃ C₁ = D₁ ∪ D₃ quantization −0.51.5 −2.5 3.5 −4.5 5.5 −6.5 7.5 −8.5 level TCQ index 0 +1 −1 +1 −1 +2 −2+2 −2 First index 0 +1 −1 +2 −2 +3 −3 +4 −4 Second index 0 1 2 3 4 5 6 78 Path 0 1 1 0 0 1 1 0 0

In addition, when the TCQ index, the first index, and the second indexare applied to an 8-coset TCQ codebook in which no zero level exists,Tables 18 through 21 can be obtained. Table 18 illustrates indexes of aunion coset A₀ formed with cosets D₀ and D₄, Table 19 illustratesindexes of a union coset A₁ formed with cosets D₁ and D₅, Table 20illustrates indexes of a union coset A₂ formed with cosets D₂ and D₆,and Table 21 illustrates indexes of a union coset A₃ formed with cosetsD₃ and D₇.

TABLE 18 Coset D₀ D₄ D₄ D₀ D₀ D₄ D₄ D₀ D₀ A₀ = D₀ ∪ D₄ quantization 0.25−1.75 2.25 −3.75 4.25 −5.75 6.25 −7.75 8.25 level TCQ index 0 −1 +1 −1+1 −2 +2 −2 +2 First index 0 −1 +1 −2 +2 −3 +3 −4 +4 Second index 0 1 23 4 5 6 7 8 Path 0 1 1 0 0 1 1 0 0

TABLE 19 Coset D₁ D₅ D₅ D₁ D₁ D₅ D₅ D₁ D₁ A₁ = D₁ ∪ D₅ quantization 0.75−1.25 2.75 −3.25 4.75 −5.25 6.75 −7.25 8.75 level TCQ index 0 −1 +1 −1+1 −2 +2 −2 +2 First index 0 −1 +1 −2 +2 −3 +3 −4 +4 Second index 0 1 23 4 5 6 7 8 Path 0 1 1 0 0 1 1 0 0

TABLE 20 Coset D₆ D₂ D₂ D₆ D₆ D₂ D₂ D₆ D₆ A₂ = D₂ ∪ D₆ quantization−0.75 1.25 −2.75 3.25 −4.75 5.25 −6.75 7.25 −8.75 level TCQ index 0 +1−1 +1 −1 +2 −2 +2 −2 First index 0 +1 −1 +2 −2 +3 −3 +4 −4 Second index0 1 2 3 4 5 6 7 8 Path 0 1 1 0 0 1 1 0 0

TABLE 21 Coset D₇ D₃ D₃ D₇ D₇ D₃ D₃ D₇ D₇ A₃ = D₃ ∪ D₇ quantization−0.25 1.75 −2.25 3.75 −4.25 5.75 −6.25 7.75 −8.25 level TCQ index 0 +1−1 +1 −1 +2 −2 +2 −2 First index 0 +1 −1 +2 −2 +3 −3 +4 −4 Second index0 1 2 3 4 5 6 7 8 Path 0 1 1 0 0 1 1 0 0

Finally, when the TCQ index, the first index, and the second index areapplied to an 8-coset TCQ codebook in which two zero levels exist,Tables 22 through 25 can be obtained. Table 22 illustrates indexes of aunion coset A₀ formed with cosets D₀ and D₄, Table 23 illustratesindexes of a union coset A₁ formed with cosets D₁ and D₅₁ Table 24illustrates indexes of a union coset A₂ formed with cosets D₂ and D₆,and Table 25 illustrates indexes of a union coset A₃ formed with cosetsD₃ and D₇.

TABLE 22 Coset D₀ D₄ D₄ D₀ D₀ D₄ D₄ D₀ D₀ A₀ = D₀ ∪ D₄ 0 −1.5 2 −3.5 4−5.5 6 −7.5 8 quantization level TCQ index 0 −1 +1 −1 +1 −2 +2 −2 +2First index 0 −1 +1 −2 +2 −3 +3 −4 +4 Second index 0 1 2 3 4 5 6 7 8Path 0 1 1 0 0 1 1 0 0

TABLE 23 Coset D₁ D₅ D₅ D₁ D₁ D₅ D₅ D₁ D₁ A₁ = D₁ ∪ D₅ 0.5 −1 2.5 −3 4.5−5 6.5 −7.5 8.5 quantization level TCQ index 0 −1 +1 −1 +1 −2 +2 −2 +2First index 0 −1 +1 −2 +2 −3 +3 −4 +4 Second index 0 1 2 3 4 5 6 7 8Coset Flag 0 1 1 0 0 1 1 0 0

TABLE 24 Coset D₆ D₂ D₂ D₆ D₆ D₂ D₂ D₆ D₆ A₂ = D₂ ∪ D₆ −0.5 1 −2.5 3−4.5 5 −6.5 7 −8.5 quantization level TCQ index 0 +1 −1 +1 −1 +2 −2 +2−2 First index 0 +1 −1 +2 −2 +3 −3 +4 −4 Second index 0 1 2 3 4 5 6 7 8Path 0 1 1 0 0 1 1 0 0

TABLE 25 Coset D₇ D₃ D₃ D₇ D₇ D₃ D₃ D₇ D₇ A₃ = D₃ ∪ D₇ 0 1.5 −2 3.5 −45.5 −6 7.5 −8 quantization level TCQ index 0 +1 −1 +1 −1 +2 −2 +2 −2First index 0 +1 −1 +2 −2 +3 −3 +4 −4 Second index 0 1 2 3 4 5 6 7 8Path 0 1 1 0 0 1 1 0 0

FIG. 18 is a block diagram of a quantization encoding apparatusaccording to an embodiment of the present invention. Referring to FIG.18, the quantization encoding apparatus according to the currentembodiment includes a quantizer 1800, an index detector 1810, and anentropy encoder 1820.

The quantizer 1800 detects quantization levels of values input throughan input terminal IN from a TCQ codebook. For example, it is assumedthat quantization is performed by means of the first index by using theconvolution encoder illustrated in FIG. 1, the trellis illustrated inFIG. 2, and the TCQ codebook illustrated in FIG. 12, when (0.6, −5.1,0.1, 1.3, −0.9, 5.8, 7.1, −1.1) are input to the quantizer 1800, thequantizer 1800 detects quantization levels (0.5, −5.5, 0.5, 1.5, −0.5,5.5, 7.5, −1.5) corresponding to the respective input values from theTCQ codebook illustrated in FIG. 12.

The index detector 1810 detects indexes containing the quantizationlevels detected by the quantizer 1800 from the TCQ codebook. The indexesdetected by the index detector 1810 correspond to the first index or thesecond index described above. In more detail, the index detector 1810detects the first index (0, −3, 0, +1, 0, +3, +4, +4, −1) containing thequantization levels (0.5, −5.5, 0.5, 1.5, −0.5, 5.5, 7.5, −1.5) detectedby the quantizer 1800 from the TCQ codebook illustrated in FIG. 12. Whenthis result is represented with bit-plane, Table 26 can be obtained.

TABLE 26 First index 0 −3 0 +1 0 +3 +4 −1 b_(S) 0 1 0 0 0 0 0 1 b₂ 0 0 00 0 0 1 0 b₁ 0 1 0 0 0 1 0 0 b₀ 0 1 0 1 0 1 0 1

The entropy encoder 1820 performs entropy encoding of the indexesdetected by the index detector 1810 and outputs the result through anoutput terminal OUT. Unlike that the TCQ index and informationindicating a path are entropy-encoded together when the TCQ index isentropy-encoded, the entropy encoder 1820 performs entropy encoding ofonly the first index or the second index without entropy encoding theinformation indicating a path.

FIG. 19 is a block diagram of a de-quantization decoding apparatusaccording to an embodiment of the present invention. Referring to FIG.19, the de-quantization decoding apparatus according to the currentembodiment includes an entropy decoder 1900, a coset detector 1910, apath detector 1920, and a quantization level detector 1930.

The entropy decoder 1900 restores indexes by demultiplexing andentropy-decoding a bitstream received from an encoder through an inputterminal IN. The indexes restored by the entropy decoder 1900 correspondto the first index or the second index.

The coset detector 1910 detects cosets contained in the indexes restoredby the entropy decoder 1900 from the TCQ codebook.

The path detector 1920 detects a coset, which matches a coset allocatedto a branch connecting a current state and a subsequent state, fromamong the cosets detected by the coset detector 1910. A branchcorresponding to the coset detected by the path detector 1920 isdetermined as a path, and a node connected to the branch becomes thesubsequent state. Unlike the TCQ index, even if the path detector 1920has not received the information on the path from the encoder, the pathcan be determined from the trellis because the first index or the secondindex is allocated by setting union cosets so that a specific branch canbe selected in a predetermined state when quantization levels areindexed in the first index or the second index. In other words, in thefirst index or the second index, since the union cosets are formed withcosets that cannot coexist with cosets allocated to branches connectedto a node of a predetermined state and the cosets allocated to branchesconnected to a node of a predetermined state are not contained in thesame union coset, a decoder can detect the path without receiving theinformation on the path.

The quantization level detector 1930 performs de-quantization bydetecting a quantization level corresponding to the coset detected bythe path detector 1920 from among the quantization levels contained inthe indexes restored by the coset detector 1910 and outputs the resultthrough an output terminal OUT. In addition to the above describedembodiments, embodiments of the present invention can also beimplemented through computer readable code/instructions in/on a medium,e.g., a computer readable medium, to control at least one processingelement to implement any above described embodiment. The medium cancorrespond to any medium/media permitting the storing and/ortransmission of the computer readable code.

The computer readable code can be recorded/transferred on a medium in avariety of ways, with examples of the medium including recording media,such as magnetic storage media (e.g., ROM, floppy disks, hard disks,etc.) and optical recording media (e.g., CD-ROMs, or DVDs), andtransmission media such as carrier waves, as well as through theInternet, for example. Thus, the medium may further be a signal, such asa resultant signal or bitstream, according to embodiments of the presentinvention. The media may also be a distributed network, so that thecomputer readable code is stored/transferred and executed in adistributed fashion. Still further, as only an example, the processingelement could include a processor or a computer processor, andprocessing elements may be distributed and/or included in a singledevice.

While aspects of the present invention has been particularly shown anddescribed with reference to differing embodiments thereof, it should beunderstood that these exemplary embodiments should be considered in adescriptive sense only and not for purposes of limitation. Any narrowingor broadening of functionality or capability of an aspect in oneembodiment should not considered as a respective broadening or narrowingof similar features in a different embodiment, i.e., descriptions offeatures or aspects within each embodiment should typically beconsidered as available for other similar features or aspects in theremaining embodiments.

Thus, although a few embodiments have been shown and described, it wouldbe appreciated by those skilled in the art that changes may be made inthese embodiments without departing from the principles and spirit ofthe invention, the scope of which is defined in the claims and theirequivalents.

1. A quantization encoding method comprising: detecting indexescorresponding to an input from a trellis coded quantization (TCQ)codebook; and entropy-encoding the detected indexes, wherein the TCQcodebook comprises branch information of a trellis state for selecting apredetermined coset and a quantization level allocated to the coset. 2.The quantization encoding method of claim 1, wherein the indexes areindexed so that cosets corresponding to branches connected to apredetermined state in a trellis cannot coexist.
 3. The quantizationencoding method of claim 2, wherein, for the indexes, positive integersare allocated to quantization levels greater than ‘0’, negative integersare allocated to quantization levels less than ‘0’, and the indexes areallocated symmetrically on ‘0’ with only different signs.
 4. Thequantization encoding method of claim 2, wherein, for the indexes, ‘0’is allocated to an index containing a smallest number of quantizationlevels by allocating only ‘0’ and positive integers as indexes, andaccording to a sequential increase of quantization levels, asequentially greater positive integer is allocated to the quantizationlevels.
 5. The quantization encoding method of claim 1-, wherein theentropy-encoding comprises not entropy encoding information of paths ofa trellis.
 6. The quantization encoding method of claim 5, wherein theindexes are indexed by using one of a two-zero-level structure, ano-zero-level structure, and a dead-zone structure.
 7. A de-quantizationdecoding method comprising: restoring indexes by performingentropy-decoding; detecting cosets included in the restored indexes froma trellis coded quantization (TCQ) codebook; detecting a coset, whichcorresponds to a branch connecting between a current state and asubsequent state from among the detected cosets, from a trellis; anddetecting a quantization level corresponding to the restored indexes andthe detected coset from the TCQ codebook.
 8. The de-quantizationdecoding method of claim 7, wherein the indexes are indexed so thatcosets corresponding to branches connected to a predetermined state inthe trellis cannot coexist.
 9. The de-quantization decoding method ofclaim 8, wherein, for the indexes, positive integers are allocated toquantization levels greater than ‘0’, negative integers are allocated toquantization levels less than ‘0’, and the indexes are allocatedsymmetrically on ‘0’ with only different signs.
 10. The de-quantizationdecoding method of claim 8, wherein, for the indexes, ‘0’ is allocatedto an index containing a smallest number of quantization levels byallocating only ‘0’ and positive integers as indexes, and according to asequential increase of quantization levels, a sequentially greaterpositive integer is allocated to the quantization levels.
 11. Thede-quantization decoding method of claim 7, wherein the indexes areindexed by using one of a two-zero-level structure, a no-zero-levelstructure, and a dead-zone structure.
 12. A method of forming aquantizer, the method comprising: setting cosets that are to be used ina trellis and a trellis coded quantization (TCQ) codebook; grouping theset cosets with cosets that cannot coexist with cosets allocated tobranches connected to predetermined states; and classifying and indexingquantization levels contained in the TCQ codebook by using the groupedcosets.
 13. The method of claim 12, wherein the setting comprisessetting a total number of cosets as 2̂n.
 14. The method of claim 12,wherein the indexing comprises allocating indexes corresponding topositive integers to quantization levels greater than ‘0’, allocatingindexes corresponding to negative integers to quantization levels lessthan ‘0’, and allocating the indexes symmetrically on ‘0’ with onlydifferent signs.
 15. The method of claim 12, wherein the indexingcomprises allocating ‘0’ to an index containing a smallest number ofquantization levels by allocating only ‘0’ and positive integers asindexes, and according to a sequential increase of quantization levels,allocating sequentially greater positive integers as indexes.
 16. Themethod of claim 12, wherein the indexing comprises performing indexingby using one of a two-zero-level structure, a no-zero-level structure,and a dead-zone structure.
 17. A quantization encoding apparatuscomprising: an index detector to detect indexes corresponding to aninput from a trellis coded quantization (TCQ) codebook; and an entropyencoder to entropy-encode the detected indexes, wherein indexes areallocated in the TCQ codebook by classifying quantization levels towhich cosets are allocated so that a coset corresponding to a specificbranch can be-selected in a predetermined state contained in a trellisby using only an index when de-quantization is performed.
 18. Thequantization encoding apparatus of claim 17, wherein the indexes areindexed so that cosets corresponding to branches connected to apredetermined state in the trellis cannot coexist.
 19. The quantizationencoding apparatus of claim 18, wherein, for the indexes, positiveintegers are allocated to quantization levels greater than ‘0’, negativeintegers are allocated to quantization levels less than ‘0’, and theindexes are allocated symmetrically on ‘0’ with only different signs.20. The quantization encoding apparatus of claim 19, wherein, for theindexes, ‘0’ is allocated to an index containing a smallest number ofquantization levels by allocating only ‘0’ and positive integers asindexes, and according to a sequential increase of quantization levels,a sequentially greater positive integer is allocated to the quantizationlevels.
 21. The quantization encoding apparatus of claim 17, wherein theentropy encoder does not entropy-encode information of paths of thetrellis.
 22. A de-quantization decoding apparatus comprising: an entropydecoder to restore indexes by performing entropy-decoding; a cosetdetector to detect cosets included in the restored indexes from atrellis coded quantization (TCQ) codebook; a path detector to detect acoset, which corresponds to a branch connecting between a current stateand a subsequent state from among the detected cosets, from a trellis;and a quantization level detector to detect a quantization levelcorresponding to the restored indexes and the detected coset from theTCQ codebook.
 23. The de-quantization decoding apparatus of claim 22,wherein the indexes are indexed so that cosets corresponding to branchesconnected to a predetermined state in the trellis cannot coexist. 24.The de-quantization decoding apparatus of claim 23, wherein, for theindexes, positive integers are allocated to quantization levels greaterthan ‘0’, negative integers are allocated to quantization levels lessthan ‘0’, and the indexes are allocated symmetrically on ‘0’ with onlydifferent signs.
 25. The de-quantization decoding apparatus of claim 23,wherein, for the indexes, ‘0’ is allocated to an index containing asmallest number of quantization levels by allocating only ‘0’ andpositive integers as indexes, and according to a sequential increase ofquantization levels, a sequentially greater positive integer isallocated to the quantization levels.
 26. An apparatus for forming aquantizer, the apparatus comprising: a coset setting unit to set cosetsthat are to be used in a trellis and a trellis coded quantization (TCQ)codebook; a coset configuration unit to group the set cosets with cosetsthat cannot coexist with cosets allocated to branches connected topredetermined states; and an indexing unit to classify and indexquantization levels contained in the TCQ codebook by using the groupedcosets.
 27. The apparatus of claim 26, wherein the coset setting unitsets a total number of cosets as 2̂n.
 28. The apparatus of claim 26,wherein the indexing unit allocates indexes corresponding to positiveintegers to quantization levels greater than ‘0’, indexes correspondingto negative integers to quantization levels less than ‘0’, and theindexes symmetrically on ‘0’ with only different signs.
 29. Theapparatus of claim 26, wherein the indexing unit allocates only ‘0’ andpositive integers as indexes, ‘0’ to an index containing a smallestnumber of quantization levels, and sequentially greater positiveintegers as indexes according to a sequential increase of quantizationlevels.